`is_tree()`

decides whether a graph is a tree, and optionally returns a
possible root vertex if the graph is a tree.

## Usage

`is_tree(graph, mode = c("out", "in", "all", "total"), details = FALSE)`

## Arguments

- graph
An igraph graph object

- mode
Whether to consider edge directions in a directed graph. ‘all’ ignores edge directions; ‘out’ requires edges to be oriented outwards from the root, ‘in’ requires edges to be oriented towards the root.

- details
Whether to return only whether the graph is a tree (

`FALSE`

) or also a possible root (`TRUE`

)

## Value

When `details`

is `FALSE`

, a logical value that indicates
whether the graph is a tree. When `details`

is `TRUE`

, a named
list with two entries:

- res
Logical value that indicates whether the graph is a tree.

- root
The root vertex of the tree; undefined if the graph is not a tree.

## Details

An undirected graph is a tree if it is connected and has no cycles. In the directed case, a possible additional requirement is that all edges are oriented away from a root (out-tree or arborescence) or all edges are oriented towards a root (in-tree or anti-arborescence). This test can be controlled using the mode parameter.

By convention, the null graph (i.e. the graph with no vertices) is considered not to be a tree.

## See also

Other trees:
`is_forest()`

,
`make_from_prufer()`

,
`sample_spanning_tree()`

,
`to_prufer()`

## Examples

```
g <- make_tree(7, 2)
is_tree(g)
#> [1] TRUE
is_tree(g, details = TRUE)
#> $res
#> [1] TRUE
#>
#> $root
#> + 1/7 vertex, from 8695cc4:
#> [1] 1
#>
```